Hi, I published an app only for beta testers, there is no production APK.
If I’m correct, it won’t affect the “30 days boost”? It starts “ticking” when an app is published first time for everybody?
From my experience yes, it should not affect your “30 days top new categories window” - though, to make sure you could simply use beta with different package.
You’re right, I’ll just go with a new package - it wouldn’t be nice to lose “top new” for game that I’ve been working for a few months 
I am not sure about Beta affecting 30 day window - reason suggests that might be the case - however you never know. Isn’t Beta essentially non-public - so only those you invite are able to see your app or something ? If so, you are not really on Google Play and it should not affect 30 day window - but Google would have to confirm this is true (or if developers here have seen that from the behavior).
Somewhat related - but publishing in Canada to test prior to release in U.S. and worldwide WILL trigger the 30 day window - this was confirmed in a Google I/O 2013 or one of their other videos i.e. the ticker starts as soon as you publish in some location.
Some games etc. used to release in Canadian market - since is similar to U.S. but smaller. That may no longer be required since now Google offers the Beta thing mentioned above - and there is also one “make app visible to a percentage of users” (which would be a partial launch - and may presumably be as a way to quickly iron out early issues from the first set of users - and also for apps which have their own servers - and may want to first gauge the impact on their servers etc.).
Yes, when you publish alpha and/or beta but there is no production version, you won’t find it in Google Play Store unless you are in group of testers (Community on Google+ or googlegroups) and you have the link from developer to sign into beta program.
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